"It was a deserved red card," said Wenger, celebrating his 400th Premier League win as Arsenal manager.

"Madness is a strong word - he didn't kill him. But he touched him and should not have done it."

Giroud will begin a three-match suspension, which includes league games against West Ham and Southampton and an FA Cup tie against Hull.

"Olivier Giroud knows he made a mistake and I know him well enough to think that he will not do it again," added Wenger, whose team are now sixth in the league.

Arsenal enjoy another Boxing Day win

Arsenal have only lost one Premier League match on Boxing Day

Alexis Sanchez (10 goals, six assists) has scored or assisted half of Arsenal's 32 Premier League goals this season

"He told me he was pushed in the back and that projected him into the keeper. Usually he's a guy who's in control of his response."

Former England striker Alan Shearer told Match of the Day: "The reason he gets angry is that Onuoha gives him a nudge, but the reaction is pathetic.

"What on earth is he doing? His team were cruising. He's been out injured for a large part of the season and now he's going to miss three games for something like that. It's just ridiculous."

Arsenal were 1-0 up thanks to Alexis Sanchez's header before Giroud's sending-off and, despite playing with 10 men for the majority of the second half, they doubled their advantage through Tomas Rosicky.

Charlie Austin set up a nervy climax, converting from the penalty spot after Mathieu Debuchy brought down Junior Holliett, but the Gunners held on to remain within touching distance of the top four.

Wenger admitted his men were nervous in the closing stages.

He said: "Our game is about psychology and the mental aspect. In the final part of the game when the result is not settled, it's always very important.

"I'm happy I could win 400 and it's not as easy as it looks. The next 400 will be much more difficult."